I think the photo you showed of the t-shirt is actually a sewn on applique, but iron on transfer is cute too, thats how I did the one I just made for a friend, but I added a few hand swen emblishments too.

I've been toying with the birthday hat idea, so far I'f thought of using stiff felt, pretty fabric with stiff interfacing, or any fabric/felt and sealing the bottom and sutffing it with pollyfill